A Test for Comparing Tail Indices for Heavy-Tailed Distributions via Empirical Likelihood

In this work, the problem of testing whether different (?2) independent samples, with (possibly) different heavy-tailed distributions, share the same extreme value index, is addressed. The test statistic proposed is inspired by the empirical likelihood methodology and consists in an ANOVA-like confrontation of Hill estimators. Asymptotic validity of this simple procedure is proved and efficiency, in terms of empirical type I error and power, is investigated through simulations under a variety of situations. Surprisingly, this topic had hardly been addressed before, and only in the two-sample case, though it can prove useful in applications.     

BANK NETWORKS AND MONETARY POLICY TRANSMISSION

This paper argues that the existence of bank networks is important for banks' reactions to monetary policy. For the example of Germany, it is found that small banks access the interbank market indirectly through the large head institutions of their respective network organizations. The interbank flows within these networks allow smaller banks to manage their funds in a fashion that helps them in keeping their loan portfolio with nonbanks relatively unaffected after a monetary contraction. This implies that tests for a bank‐lending channel in countries with comparable bank networks should not rely on a size criterion only, and explains why several recent contributions have found a prominent role for banks' liquidity positions. (JEL: C32, E52, G21)     

LARGE AND MODERATE DEVIATIONS PRINCIPLES FOR KERNEL ESTIMATION OF A MULTIVARIATE DENSITY AND ITS PARTIAL DERIVATIVES

This paper studies the large deviations behaviour of the kernel estimator of a probability density f, by considering the case when the kernel takes negative values. It establishes large and moderate deviations principles for the kernel estimators of the partial derivatives of f. The estimators of the derivatives exhibit a quadratic behaviour for both the large and the moderate deviations scales, whereas for the density estimator there is a classical gap between the large deviations and the moderate deviations asymptotics.     

Empirical likelihood based confidence regions for first order parameters of heavy-tailed distributions

Let X₁,…,X_n be some i.i.d. observations from a heavy-tailed distribution F, i.e. the common distribution of the excesses over a high threshold u_n can be approximated by a generalized Pareto distribution G_γ,σn with γ>0. This paper deals with the problem of finding confidence regions for the couple (γ,σ_n): combining the empirical likelihood methodology with estimation equations (close but not identical to the likelihood equations) introduced by Zhang (2007), asymptotically valid confidence regions for (γ,σ_n) are obtained and proved to perform better than Wald-type confidence regions (especially those derived from the asymptotic normality of the maximum likelihood estimators). By profiling out the scale parameter, confidence intervals for the tail index are also derived.